The difference is that balloons are inflated through a hole in the bottom, but knowledge expands by some kind of osmosis across the boundary with the unknown. Ideas on the outside surface are accessible and can be acquired by the learner, but ideas further away cannot be understood. The upshot of this is that the more you know, the more things there are out there that you could learn about. Also, you realize there are more things that exist but you don't understand them.

The model discussed the learning of already-studied topics, but it seems applicable to the study of new topics too. I imagine more energy is required to transport the knowledge across the membrane, in this case. (Sure, this stretches the analogy somewhat. It gets worse, too.)

Sharing knowledge

When two mappers (of MappersVsPackers) meet, they need to establish a common vocabulary in order to discuss a topic. The process is described in the ProgrammersStone as making a mapping (abstract mathematical sense) between the ideas in the two minds, usually by sampling points at intervals and describing the surroundings until the two people agree that their maps agree. Then they can have a discussion.

This can be done verbally (and apparently without realizing you're doing it), or as a BrainDump? onto paper in the form of a MindMap.

Mappings between volumes are awkward

Suddenly the idea of trying to draw two volumes (the balloon-like minds of two people) and plot the lines mapping equivalent concepts seems quite tricky. PeteSmith? suggested dropping a spare dimension, since it is causing the trouble.

Now we can talk about a flat circle, at which knowledge is absorbed at the circumference. If you had a large sheet of paper, you could write out all the things you know, then stick it on the wall next to someone else's. Put some drawing pins in the landmark ideas and join the dots with colored string, and you've got a fairly easy-to-understand relationship between two minds.

IdeaSpace is not flat, homogenous and circular

Going in the opposite direction, MatthewAstley states without proof 8-) that the space in which your ideas exist is an irregular fractal hypersponge.

Fractal because most topics can be known or researched in an arbitrary amount of detail, and still not covered completely.

Hyperdimensional because ideas that seem far apart can actually be quite close if you look at them from another side, and there are many different ways of interconnecting or carving them. (cf. the LogicalKnife? wielded by Phaedrus of ZenAndTheArtOfMotorcycleMaintenance.)

A sponge because you can never fill it.

Nail them to the wall

If you want to understand butterflies' patterning, the obvious way to go about it is to catch lots of them and nail them to the wall in some kind of order.

Wikis around the world are steaming ahead with the CollectAndOrganize (or CollectAndSummarize?) phase. Exactly how these things could be meshed together, so that the related ideas overlap neatly, is currently beyond us.

Practical applications

None that I know of. This will have to be fixed eventually, if only to avoid the dreaded GreyGoo.

As work is done on things like SemanticWeb and NooWiki, there will be growing piles of data tied together in neat structures. I need to find out more about these...

As I trundle round this wiki, the DebianGnuLinux packaging system and other InterTwingled structures, I'm scribbling notes on scraps of paper in the vain hope that I can bring it all together into something useful. -- MatthewAstley